Fifth dimension

In physics and mathematics, a sequence of "N" numbers can be understood to represent a location in an "N"-dimensional space. When "N"=5, the space consisting of all such locations is called the fifth dimension.

Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics.

In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three spatial and one time dimensions; e.g. physicists have speculated that the graviton, a particle thought to carry the force of gravity, may "leak" into the fifth or higher dimensions which would explain how gravity is significantly weaker than the other three fundamental forces. The Kaluza-Klein theory used a fifth dimension to unify gravity with the electromagnetic force, and now is seen as essentially a gauge theory with gauge group the circle group. M-theory suggests that space-time has eleven dimensions, seven of which are "rolled up" to below the subatomic level.

In 1993 the physicist Gerard 't Hooft put forward the holographic principle, which explains that the "information about an extra dimension is visible as a curvature in a spacetime with one fewer dimensions". For example, holograms are three-dimensional pictures placed on a two-dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the "spacetime fabric".

It has occasionally been stated Who|date=September 2008 the fifth dimension is probability, meaning that the fifth dimension is the full amount of possibilities that could happen or, in other words, alternate realities. Fact|date=September 2008

Five-dimensional geometry

Polytopes

In five or more dimensions, only three regular polytopes exist. For "N" dimensions, they are:

# The simplex, with "N"+1 vertices, all at equal distances from one another; it consists of "N"+1 simplices of dimension "N"-1. The three-dimensional simplex is the tetrahedron, and the five-dimensional simplex is a hexatetron; it has 6 vertices, 15 edges, 20 faces (each a triangle), 15 cells (or solids - each a tetrahedron), and 6 hypercells (each a pentachoron).
# The hypercubes, having 2^"N" vertices whose coordinates may be written (±1,±1, ..., ±1) for some suitable set of axes. It consists of 2"N" hypercubes of the next lower dimension. The five-dimensional hypercube is a decateron or penteract; it has 32 vertices, 80 edges, 80 faces (each a square), 40 cells (each a cube), and 10 hypercells (each a tesseract).
# The cross polytope, with 2"N" vertices, paired on opposite sides of the "N" coordinate axes; it consists of 2^"N" simplices of dimension "N"-1. The five-dimensional cross polytope is a triacontakaiditeron or pentacross, with 10 vertices, 40 edges, 80 faces (each a triangle), 80 cells (each a tetrahedron), and 32 hypercells (each a pentachoron).

The dual of a simplex is a simplex. The hypercube and cross-polytope of the same dimension are dual to each other.

Here are three projected images of the edges of a regular decateron or penteract:

See also: 5-polytope, and List of regular 5-polytopes

Hypersphere

The hypervolume of a Hypersphere in 5-space is::$V=frac\{8pi\; ^2r^5\}\{15\}$

The "Fifth dimension" in popular culture

*In the fictitious universe of DC Comics, the "Fifth dimension" is the place from which Mister Mxyzptlk comes.
*In 1966, The Byrds released an album titled "Fifth Dimension", in which the fifth dimension is a metaphor for unexplored and unknown aspects of the universe and oneself.
*The novel "The Boy Who Reversed Himself" features four and five-dimensional space, referred to as 4-space and 5-space.
*The hard science fiction novel "Diaspora" by Greg Egan features a series of ten dimensional universes arrayed inverse to one another, wherein every odd universe has four "macro" dimensions, three space plus one time, and six "submicro" dimensions, manifesting as a 6-sphere per every Planck distance, but which are "themselves" another ten dimensional universe, featuring six macro dimensions, five space plus one time, and four submicro dimensions per every Planck distance. A substantial portion of the novel depicts daily life and physics in such a universe, which differs substantially due to the peculiar physics hypothesis Egan formulated for the novel.
*Rod Serling's "The Twilight Zone" television series intro included the line, "There is a Fifth Dimension, beyond that which is known to man."
*In the first episode of "Doctor Who", Ian Chesterton was teaching his class about the three dimensions when Susan Foreman, his student and the Doctor's granddaughter, corrected him to say there were in fact five dimensions. He agreed the fourth was time, and asked her about the fifth, to which she replied it was 'space'.
*There is a fictional book, "Hyperspace", in a series called 'Choose Your Own Adventure'
*The characters in Madeleine L'Engle's novel, "A Wrinkle In Time" use the fifth dimension to travel through space.
*In the children's television program "Mona the Vampire", there is an amusement park ride called the "Fifth Dimensia"
*Rob Bryanton's book and animation "Imagining the Tenth Dimension" advances the idea that our fourth-dimensional "line of time" is being created one planck length at a time from the available probalistic branches within the fifth dimension.
*The Fifth Dimension was a popular soul/pop group in the late 60's starring Marilyn McCoo and Billy Davis and featured such hits as "Wedding Bell Blues", Stoned Soul Picnic", "Up, Up, and Away", "Aquarius", and many others...
*The fifth dimension of love of the Divine is termed by the Gaudiya Vaisnavas in Hindu philosophy as turyatita, the dimension of the soul's Soul.
* The fifth dimension is mentioned in the book, Mostly Harmless, from the series entitled The Hitchhiker's Guide to the Galaxy, by Douglas Adams.
*"Fifth Dimension" is a radio drama adaption of the short story, "The Plattner Story" by H. G. Wells, produced by the Radio Tales series for National Public Radio. This science fiction program was produced and script edited by series producer Winnie Waldron, who also served as the on-air host. The program was narrated by actress Winifred Phillips, who also composed the musical score. The program aired in the United States via NPR Playhouse on September 5, 2000, and currently airs in reruns on Sonic Theater channel 163 of XM Satellite Radio.

ee also

*5-manifold
*Hypersphere
*Dimension
*Fourth dimension

External links

* [http://robertinventor.com/software/virtualflower/virtualflower/tesseract.htm Anaglyph of a five dimensional hypercube in hyper perspective]
* [http://www.5thdth.com/waleed/theory.htm Another theory of 5th Dimension done by M. Helmy Said]
* [http://www.rmcybernetics.com/science/physics/dimensions.htm Other Dimensions of the Universe]